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”Beam Dynamics for Nb3Sn dipoles ... latest news". Bernhard Holzer. IP5. IR 7. IP8. IP1. IP2. *. DS Upgrade Scenarios. halo. Shift 12 Cryo -magnets, DFB, and connection cryostat in each DS. transversely shifted by 4.5 cm. halo. New ~3..3.5 m shorter Nb 3 Sn Dipoles (2 per DS). - PowerPoint PPT Presentation
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Bernhard Holzer
*
IP5
IP1IP2
IP8
IR 7
”Beam Dynamics for Nb3Sn dipoles ... latest news"
2
DS Upgrade Scenarios
M. Karppinen TE-MSC-ML
-4.5 m shifted in s
halo
+4.5 m shifted in s
transversely shifted by 4.5 cm
halo
Shift 12 Cryo-magnets, DFB, and connection cryostat in each DS
New ~3..3.5 m shorter Nb3Sn Dipoles (2 per DS)
May 2, 2011
Effects to be expected:
* magnets are shorter than MB Standards change of geometry distortion of design orbit
* R-Bends S-Bends edge focusing distortion of the optics tune shift, beta beat
* nonlinar transfer function (3.5 TeV) distortion of closed orbitto be corrected locally ??dedicated corrector coils ??trim power supply ??
* feed down effects from sagitta ?
* multipole effect on dynamic aperture ?
Sixtrack Tracking Simulations
Comparison: b3 Hysteresis Nb3Sn / NbTiM. Karppinen
The persistent current problem: Very First Multipole Estimates
b3 remanence as a function of precycle (pre-injection plateau) B. Auchmann
tracking studies & prototype measurements needed
Systematic errorsCurrent
(A) B1 b2 b3 b4 b5 b6 b7763 -0.7325 2.50 13.96 0.02 -0.24 0.00 0.29
1456 -1.3977 2.50 13.96 0.02 -0.24 0.00 0.292149 -2.0628 2.50 13.96 0.02 -0.24 0.00 0.292842 -2.7279 2.50 13.96 0.02 -0.24 0.00 0.293535 -3.3930 2.50 13.96 0.02 -0.24 0.00 0.294228 -4.0581 2.49 13.96 0.02 -0.24 0.00 0.294921 -4.7231 2.48 13.97 0.02 -0.24 0.00 0.295614 -5.3875 2.45 13.99 0.02 -0.23 0.00 0.296307 -6.0499 2.28 14.03 0.01 -0.23 0.00 0.297000 -6.7075 1.84 14.15 -0.01 -0.23 0.00 0.297692 -7.3565 1.05 14.31 -0.04 -0.21 0.00 0.298385 -7.9928 -0.21 14.36 -0.10 -0.18 0.00 0.299078 -8.6120 -2.13 14.21 -0.21 -0.17 -0.01 0.299771 -9.2204 -4.43 13.97 -0.31 -0.15 -0.01 0.29
10464 -9.8212 -6.94 13.68 -0.41 -0.14 -0.02 0.2911157 -10.4160 -9.68 13.37 -0.51 -0.13 -0.02 0.3011850 -11.0060 -12.49 13.06 -0.58 -0.13 -0.02 0.30
Nb3Sn Dipole: Multipole Errors, “Pure Estimation !!”
... in the usual units, i.e. 10 -4 referred to the usual ref radius = 17mm
Nb3Sn Dipole: Multipole Errors, “Pure Estimation !!”
NbTi Dipole: Multipole Errors:
Where are we ? IP1,2,5,IP7
Q8 Q9 Q10
Present Option: 2 x 5.5m Nb3Sn Dipoles separated
optics situationcollision optics, 7 TeV
no big difference in optical functions between injection / luminosity
b3 = 98, full & local correctionb3 = 98, no correction
ideal, linear machine
theory: phase space ellipse defined by optical parameters
Tracking Studies: Dynamic Aperture determined via stability / survival time
strong b3 multipole
Phase Space Distance
Tracking Studies: Dynamic Aperture determined via survival time
b3 = 98, no correction
survival time ... measured in number of turns ... gives an indication of the influence
of the non-linear fields on the ( an- ) harmonic oscillation of the particles.
x
yFor the experts: 60 seeds, 10^5 turns, 4-18 σ in units of 2, 30 particle pairs, 17 angles
Field Quality: Dynamic Aperture Studies7 TeV Case, luminosity optics (55cm)
ε=5*10-10 radm ( εn = 3.75μm)
ideal Nb3Sn dipolesmult. coeff. à la error table6
at high field the higher harmonics are small enough,the p.c. effects disappeared and the emittance is reduced (Liouville)
dynamic aperture for Nb3Sn
full error table (blue) b3 = 0an = bn = 0
Field Quality: Dynamic Aperture Studiesinjection optics, 450 GeV,influence of b3 values, 2 IP’s = 8 dipoles
dyn aperture injection optics, minimum of 60 seeds
the first estimated errors lead to
extreme reduction in dyn. aperture
main problem: b 3
dynamic aperture for Nb3Sn case: full error table (red) b3 reduced to 50% (green)b3 reduced to 25% (violett)b3 = 0 and to compare with: present LHC injection
for the experts: unlike to the collision case: at injection the b3 of the Nb3Sn dipoles is the driving force to the limit in dynamic aperture.A scan in b3 values has been performed and shows that values up to b3 ≈ 20 units are ok.
Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, Scan of b3
dyn aperture injection optics, minimum of 60 seeds
Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, Different Sectors
#2,7, an=bn=0
#1,2,5 b3=27#2,7 b3=27
#2,7 first estimate, “error table 2”
dyn aperture for Nb3Sn dipoles in #2,7 and in #1,2,5standard spool piece correctors
optimised for Q’ correction per octant
Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, ATS
#1,2,5 bn=20
#1,2,5 b3=0
#1,2,5 b3=27
#1,2,5 an=bn=0
dyn aperture for Nb3Sn dipoles #1,2,5ATS shows a increased sensitivity for higher multipoles, -> tighter limit for b3
and higher an / bn ATS Lattice
5.5 m 11 T Dipole Error Table Iinj Inom StdevB0 -0.758 -11.217 B/I -1.001 -0.947 Lmag 5300 5300 b2 -0.80 -14.41 1.93b3 41.33 5.20 1.24b4 0.09 -0.45 0.60b5 6.90 0.51 0.31b6 0.01 -0.02 0.18b7 -0.10 0.10 0.11b8 0.00 0.00 0.06b9 1.31 0.94 0.03b10 0.00 0.00 0.01b11 0.33 0.43 0.01b12 0.00 0.00 b13 0.00 0.00 a1 0.87 4.02 2.87a2 -0.02 -0.26 1.66a3 -0.11 -0.08 1.00a4 0.00 -0.01 0.64a5 0.09 0.09 0.38a6 0.00 0.00 0.20a7 0.03 0.03 0.09a8 0.00 0.00 0.05a9 0.00 0.00 0.03a10 0.00 0.00 0.02a11 0.00 0.00 0.01a12 0.00 0.00 a13 0.00 0.00
Current Strength b1 b2 b3 b4 b5 b6
762.8948 0.746 104 -8.752 -23.648 2.856 6.020 -2.782
1.00E+03 0.983 104 -8.218 -37.815 -0.535 4.431 -4.096
a1 a2 a3 a4 a5 a6
0.0 14.981 -5.100 -6.927 1.632 7.834
0.0 48.483 0.924 0.392 2.680 11.107measured values for the “systematics”
FNAL
best guess for the ramndom errors
Mikko et al
Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, first measured values: “FNAL-demo-2”
ideal Nb3Sn dipoles,an=bn=0
first FNAL prototype systematics& Mikkos random artificially enhanced
b4...6 , a3
Field Quality: Dynamic Aperture StudiesInjection Optics, 450 GeV, first measured values: “FNAL-demo-2”
and again the tracking ...
systematics -> FNAL prototyperandom -> best guessuncertainty - > MB standard dipole
first measured values are just at the limit but at the moment in sufficient dynamic aperture is obtained.
Preliminary (!) Resumée:
first estimates / calculations for pc systematics ... where chilling
limits calculated for higher multipole coefficients (mainly b3)
first measurement results are “just within” these limits
problem: injection energy / opticslarge emittance, large p.c. effects
ATS injection / luminosity seems a bit more sensitive than LHC standard optics
unknown: realistic values for random errors ? do we have to deal with uncertainties ? limits for individual higher coefficients
Plan & Next Steps: follow up closely the new results
Particle Tracking Calculations
particle vector: field at particle position
x
x
)( 2221 zxg
xzgB
calculate kick on the particle
€
Δ x 1 =Bzlp /e
= 12
′ g p /e
l(x12 − z1
2) = 12
msextl(x12 − z1
2)
1111
1 //zlxml
epzxg
eplBz sext
x
Δ
Δ
xx
xxx
1
1
1
1
Δ
11
1
1
1
zzz
zz
and continue with the linear matrix transformations
Idea: calculate the particle coordiantes x, x´ through the linear lattice … using the matrix formalism. if you encounter a nonlinear element (e.g. sextupole): stop calculate explicitly the magnetic field at the particles coordinate